In Yii2 you can access the identity interface for the current user by using the identityInterface object from within the \\yii\\web\\User class with something like this
Okay it seems this was removed intentionally to avoid "confusion". See https://github.com/yiisoft/yii2/issues/167. So the only way to do this by calling the session class directly.
\Yii::$app->session->set('user.attribute',$value);
\Yii::$app->session->get('user.some_attribute');
Because it now stored directly in session without prefix it is best to namespace the keys with identifiers like user.xxxx
to avoid collision with some other key set at different point of the application.